Question: Factor completely. $81p^2-144pq+64q^2=$
Explanation: $\begin{aligned} &\phantom{=}81 p ^2 - 144 p q + 64 q ^2 \\\\ &= ({9 p })^2 - 2({9 p })({8 q })+({8 q })^2 \end{aligned}$ Using the square of a difference pattern: $\begin{aligned} &\phantom{=}({9 p })^2 - 2({9 p })({8 q })+({8 q })^2 \\\\ &=({9 p } - {8 q })^2 \end{aligned}$ In conclusion, $81 p ^2 - 144 p q + 64 q ^2=(9 p - 8 q )^2$ Remember that you can always check your factorization by expanding it.